This is a Produx pocket calculator. It was designed by Otto Neuter and produced in Germany starting in the 1930s. I suspect this particular one was from the 1950s or maybe `60s, due to the coloring and the reference to West Germany on the back.
To add, insert a stylus in the number for the appropriate column *below* the totals, and slide downward. If the addition (I added 5) overflows, the corresponding column in the total turns red, alerting you that you need to go up and around the "shepherd's hook" to carry the one.
To subtract, find the correct column/number *above* the total and slide *up*. If you underflow, the total in that column turns red so you go down and around that shepherd's hook to deduct from the column left of it. Here I subtracted 50.
As you add, a bar extends from the bottom for that column and as you subtract, it retracts. To zero everything out, you push all of the protruding bars back into the case. The overall design is actually pretty nice, especially considering the small size of the calculator.